, 92:76 | Cite as

High-sensitivity measurement of Rydberg population via two-photon excitation in atomic vapour using optical heterodyne detection technique

  • Arup BhowmickEmail author
  • Dushmanta Kara
  • Ashok K Mohapatra


We demonstrate a technique based on optical heterodyne detection to measure the Rydberg population in the thermal atomic vapour. The technique used a probe beam far off-resonant to the D2 line of rubidium along with a reference beam with frequency offset by 800 MHz in the presence of a coupling laser that couples to Rydberg state via two-photon resonance. The polarisation of the probe, reference and coupling beams are suitably chosen such that only the probe beam goes through a nonlinear phase shift due to the two-photon process which is measured relative to the phase shift of the reference beam using optical heterodyne detection technique. We show that the technique has a sensitivity to measure the minimum phase shift of the order of a few \(\mu \)rad. We have used a suitable model of two-photon excitation of a three-level atom to show that the minimum phase shift measured in our experiment corresponds to the Rydberg population of the order of \(10^{-5}\). The corresponding probe absorption for the given laser parameters is of the order of \(10^{-7}\). We demonstrate that this technique is insensitive to polarisation impurity or fluctuations in the beams. The technique is particularly useful in measuring the Rydberg population via two-photon excitation in thermal vapour where microchannel plates (MCP) could be relatively difficult to implement. It can also be used in the ultracold atomic sample with suitable laser parameters.


Heterodyne Rydberg population two-photon atomic vapour dispersion 


42.50.Nn 32.80.Rm 42.50.Gy 34.20.Cf 



The authors acknowledge Sushree S Sahoo and Snigdha S Pati for their assistance in performing the experiment. This experiment was financially supported by the Department of Atomic Energy, Government of India.


  1. 1.
    D Jaksch, J I Cirac, P Zoller, S L Rolston, R Côté and M D Lukin, Phys. Rev. Lett. 85, 2208 (2000)ADSCrossRefGoogle Scholar
  2. 2.
    M D Lukin, M Fleischhauer, R Côté, L M Duan, D Jaksch, J I Cirac and P Zoller, Phys. Rev. Lett. 87, 037901 (2001)ADSCrossRefGoogle Scholar
  3. 3.
    L Isenhower, E Urban, X L Zhang, A T Gill, T Henage, T A Johnson, T G Walker and M Saffman, Phys. Rev. Lett. 104, 010503 (2010)ADSCrossRefGoogle Scholar
  4. 4.
    T Wilk, A. Gaëtan, C Evellin, J Wolters, Y Miroshnychenko, P Grangier and A Browaeys, Phys. Rev. Lett. 104, 010502 (2010)ADSCrossRefGoogle Scholar
  5. 5.
    I Friedler, D Petrosyan, M Fleischhauer and G Kurizki, Phys. Rev. A 72, 043803 (2005)ADSCrossRefGoogle Scholar
  6. 6.
    M Saffman and T G Walker, Phys. Rev. A 66, 065403 (2002)ADSCrossRefGoogle Scholar
  7. 7.
    Y O Dudin and A Kuzmich, Science 336, 887 (2012)ADSCrossRefGoogle Scholar
  8. 8.
    Y Du, Y Zhang, C Zuo, C Li, Z Nie, H Zheng, M Shi, R Wang, J Song, K Lu and M Xiao, Phys. Rev. A 79, 063839 (2009)ADSCrossRefGoogle Scholar
  9. 9.
    J Che, J Ma, H Zheng, Z Zhang, X Yao, Y Zhang and Y Zhang, Europhys. Lett. 109, 33001 (2015)ADSCrossRefGoogle Scholar
  10. 10.
    Z Zhang, J Che, D Zhang, Z Liu, X Wang and Y Zhang, Opt. Express 23, 13814 (2015)ADSCrossRefGoogle Scholar
  11. 11.
    Y Zhang, Z Wang, Z Nie, C Li, H Chen, K Lu and M Xiao, Phys. Rev. Lett. 106, 093904 (2011)ADSCrossRefGoogle Scholar
  12. 12.
    S Chatterjee, A Saha and B Talukdar, Pramana – J. Phys. 86, 861 (2016)ADSCrossRefGoogle Scholar
  13. 13.
    H Weimer, R Löw, T Pfau and H P Büchler, Phys. Rev. Lett. 101, 250601 (2008)ADSCrossRefGoogle Scholar
  14. 14.
    T Pohl, E Demler and M D Lukin, Phys. Rev. Lett. 104, 043002 (2010)ADSCrossRefGoogle Scholar
  15. 15.
    G Pupillo, A Micheli, M Boninsegni, I Lesanovsky and P Zoller, Phys. Rev. Lett. 104, 223002 (2010)ADSCrossRefGoogle Scholar
  16. 16.
    N Henkel, R Nath and T Pohl, Phys. Rev. Lett.  104, 195302 (2010)ADSCrossRefGoogle Scholar
  17. 17.
    A Angelone, F Mezzacapo and G Pupillo, Phys. Rev. Lett. 116, 135303 (2016)ADSCrossRefGoogle Scholar
  18. 18.
    D Tong, S M Farooqi, J Stanojevic, S Krishnan, Y P Zhang, R Côté, E E Eyler and P L Gould, Phys. Rev. Lett. 93, 063001 (2004)ADSCrossRefGoogle Scholar
  19. 19.
    K M Singer, M Reetz-Lamour, T Amthor, L G Marcassa and M Weidemüller, Phys. Rev. Lett. 93, 163001 (2004)ADSCrossRefGoogle Scholar
  20. 20.
    T Cubel Liebisch, A Reinhard, P R Berman and G Raithel, Phys. Rev. Lett. 95, 253002 (2005)ADSCrossRefGoogle Scholar
  21. 21.
    T Vogt, M Viteau, J Zhao, A Chotia, D Comparat and P Pillet, Phys. Rev. Lett. 97, 083003 (2006)ADSCrossRefGoogle Scholar
  22. 22.
    R Heidemann, U Raitzsch, V Bendkowsky, B Butscher, R Löw, L Santos and T Pfau, Phys. Rev. Lett. 99, 163601 (2007)ADSCrossRefGoogle Scholar
  23. 23.
    U Raitzsch, V Bendkowsky, R Heidemann, B Butscher, R Löw and T Pfau, Phys. Rev. Lett. 100, 013002 (2008)ADSCrossRefGoogle Scholar
  24. 24.
    E Urban, T A Jojnson, T Henage, L Isenhower, D D Yavuz, T G Walker and M Saffman, Nature Phys. 5, 110 (2009)CrossRefGoogle Scholar
  25. 25.
    A Gaëtan, Y Miroshnychenko, T Wilk, A Chotia, M Viteau, D Comparat, P Pillet, A Browaeys and P Grangier, Nature Phys. 5, 115 (2009)CrossRefGoogle Scholar
  26. 26.
    Y O Dudin, L Li, F Bariani and A Kuzmich, Nature Phys. 8, 790 (2012)CrossRefGoogle Scholar
  27. 27.
    P Schauss, M Cheneau, M Endres, T Fukuhara, S Hild, A Omran, T Pohl, C Gross, S Kuhr and I Bloch, Nature 491, 87 (2012)ADSCrossRefGoogle Scholar
  28. 28.
    J D Pritchard, D Maxwell, A Gauguet, K J Weatherill, M P A Jones and C S Adams, Phys. Rev. Lett. 105, 193603 (2010)ADSCrossRefGoogle Scholar
  29. 29.
    T Peyronel, O Firstenberg, Q-Y Liang, S Hofferberth, A V Gorshkov, T Pohl, M D Lukin and V Vuletic̀, Nature 488, 57 (2012)ADSCrossRefGoogle Scholar
  30. 30.
    O Firstenberg, T Peyronel, Q-Y Liang, A V Gorshkov, M D Lukin and V Vuletié, Nature 502, 71 (2013)ADSCrossRefGoogle Scholar
  31. 31.
    V Parigi, E Bimbard, J Stanojevic, A J Hilliard, F Nogrette, R Tualle-Brouri, A Ourjoumtsev and P Grangier, Phys. Rev. Lett. 109, 233602 (2012)ADSCrossRefGoogle Scholar
  32. 32.
    T M Weber, M Höning, T Niederprüm, T Manthey, O Thomas, V Guarrera, M Fleischhauer, G Barontini and H Ott, Nature Phys. 11, 157 (2015)ADSCrossRefGoogle Scholar
  33. 33.
    Y-Y Jau, A M Hankin, T Keating, I H Deutsch and G W Biedermann, Nature Phys.  12, 71 (2016)CrossRefGoogle Scholar
  34. 34.
    D Cano and J Fortágh, Phys. Rev. A 80, 043413 (2014)ADSCrossRefGoogle Scholar
  35. 35.
    H Labubu, S Ravels, D Barredo, L. Béguin, F Nogrette, T Lahaye and A Browaeys, Phys. Rev. A 90, 023415 (2014)ADSCrossRefGoogle Scholar
  36. 36.
    F Karlewski, M Mack, J Grimmel, N Sádor and J Fortágh, Phys. Rev. A 91, 043422 (2015)ADSCrossRefGoogle Scholar
  37. 37.
    W Sandner, G A Ruff, V Lange and V Eichmann, Phys. Rev. A 32, 3794 (1985)ADSCrossRefGoogle Scholar
  38. 38.
    M M Valado, N Malossi, S Scotto, D Ciampini, E Arimondo and O Morsch, Phys. Rev. A 88, 045401 (2013)ADSCrossRefGoogle Scholar
  39. 39.
    A K Mohapatra, T R Jackson and C S Adams, Phys. Rev. Lett. 98, 113003 (2007)ADSCrossRefGoogle Scholar
  40. 40.
    A K Mohapatra, M G Bason, B Butscher, K J Weatherill and C S Adams, Nature Phys. 4, 890 (2008)ADSCrossRefGoogle Scholar
  41. 41.
    C Carr, R Ritter, C G Wade, C S Adams and K J Weatherill, Phys. Rev. Lett. 111, 113901 (2013)ADSCrossRefGoogle Scholar
  42. 42.
    T Baluktsian, B Huber, R Löw and T Pfau, Phys. Rev. Lett. 110, 123001 (2013)ADSCrossRefGoogle Scholar
  43. 43.
    A K Kölle, G Epple, H. Kübler, R Löw and T Pfau, Phys. Rev. A 85, 063821 (2012)ADSCrossRefGoogle Scholar
  44. 44.
    Z Zhang, H Zheng, X Yao, Y Tian, J Che, X Wang, D Zhu, Y Zhang and M Xiao, Sci. Rep. 5, 10462 (2015)ADSCrossRefGoogle Scholar
  45. 45.
    D Barredo, H Kübler, R Daschner, R Löw and T Pfau, Phys. Rev. Lett. 110, 123002 (2013)ADSCrossRefGoogle Scholar
  46. 46.
    A M Akulshin, A I Sidorov, R J McLean and P Hannaford, J. Opt. B: Quantum Semiclass Opt. 6, 491 (2004)ADSCrossRefGoogle Scholar
  47. 47.
    A Bhowmick, S S Sahoo and A K Mohapatra, Phys. Rev. A 94, 023839 (2016)ADSCrossRefGoogle Scholar
  48. 48.
    H Kübler, J P Shaffer, T Baluktsian, R. Löw and T Pfau, Nature Photon. 4, 112 (2010)ADSCrossRefGoogle Scholar
  49. 49.
    O Firstenberg, C S Adams and S Hofferberth, J. Phys. B: At. Mol. Opt. Phys. 49, 152003 (2016)ADSCrossRefGoogle Scholar
  50. 50.
    G Müller, A Witch, R Rinkleff and K Danzmann, Opt. Commun. 127, 37 (1996)ADSCrossRefGoogle Scholar
  51. 51.
    A M Akulshin, S Barreiro and A Lezama, Phys. Rev. Lett. 83, 4277 (1999)ADSCrossRefGoogle Scholar
  52. 52.
    H Kang and Y Zhu, Phys. Rev. Lett. 91, 093601 (2003)ADSCrossRefGoogle Scholar
  53. 53.
    H Y Lo, P C Su and Y F Chen, Phys. Rev. A 81, 053829 (2010)ADSCrossRefGoogle Scholar
  54. 54.
    Y Han, J Xiao, Y Liu, C Zhang, H Wang, M Xiao and K Peng, Phys. Rev. A 77, 023824 (2008)ADSCrossRefGoogle Scholar
  55. 55.
    The probe Rabi frequency is estimated using the relation with the intensity of probe as \(I/I_{{\rm sat}}=2|\Omega _{{\rm p}}|^2/\Gamma ^2\). For 85Rb, \(I_{{\rm sat}}=1.64\) mW\(/\)cm2 and \(\Gamma =2\pi \times 6\) MHz. Coupling Rabi frequency is estimated by fitting the Rydberg EIT signal with a weak probe beam without focussing and then scaling it with the intensity of the beamGoogle Scholar
  56. 56.
    R Han, H K Ng and B G Englert, J. Mod. Opt. 60, 255 (2013)ADSCrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  • Arup Bhowmick
    • 1
    Email author
  • Dushmanta Kara
    • 1
  • Ashok K Mohapatra
    • 1
  1. 1.School of Physical SciencesNational Institute of Science Education and Research Bhubaneswar, HBNIKhurdaIndia

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